1. Introduction
Magnetic resonance imaging (MRI) is widely used in medicine and other applications for performing three-dimensional imaging, for example of a human body (or part of a human body). In some cases, the MRI imaging may be performed in real-time to provide real-time (dynamic) visual feedback to a surgeon during a medical procedure, such as neuro-surgery.
It is well-known that certain forms of MRI, such as echo planar imaging (EPI) are subject to susceptibility artefacts, inaccuracies in intensity and geometry caused by inhomogeneities in the magnetic field (sometimes referred to as B0 inhomogeneities). Such inhomogeneities may arise at the transition between two forms of matter having different magnetic properties (magnetic susceptibility), for example at the transition between the brain and surrounding air or bone. These inaccuracies can result in anatomical features being incorrectly located in an image, in other words, the positions of such features may be distorted from their true locations. This distortion can be very significant, for example, in real-time MRI imaging for image-guided surgery, where it is extremely important to know the precise location of a medical instrument in respect to the different anatomical features—otherwise (for example) a treatment may be applied to the wrong location, or the medical instrument may inadvertently damage some other component of the body.
Existing techniques for addressing the problem of B0 inhomogeneities are generally divided into two categories. A first category is based in effect on image analysis, without consideration of the underlying physics. In this category, it is assumed that a prior image of the relevant region of the body is available which does not suffer from B0 inhomogeneities—such an image will therefore be undistorted. Such an undistorted image can be obtained from various MRI imaging techniques, for example, T1 images. A registration or mapping is then produced based on identifying features in the (potentially) distorted image with similar looking features in the undistorted image. This then allows the distorted image to be warped or transformed to coincide in positional terms with the undistorted image. In other words, a given feature (X) in the distorted image is identified with the same feature (X′) in the undistorted image. The distorted image is then transformed (un-distorted) so that X now becomes coincident with (or at least close to) X′. This new positioning is assumed to represent the correct (true) location of the anatomical feature corresponding to X. One drawback with this image intensity mapping is that it relies upon the image containing sharp (distinct), well-identified features. However, if no (or only a few) such features are present in the image, for example, the image appears rather homogenous, then it is difficult to perform the desired registration and subsequent transformation. A further drawback is that this method relies upon the availability of an existing undistorted image.
A second category of technique for addressing the problem of B0 inhomogeneities is more physics-based, in that it tries to calculate the actual distortions arising from the B0 inhomogeneities, and then to remove (cancel out) these distortions. A MRI signal strength at any given can be represented as a complex quantity S=ke(iθ), where k is the absolute magnitude or intensity of the signal, and θ is the phase. Although most MRI imaging is based on the intensity k, it is known to use the phase θ to generate a field map, which can then be used to remove from the image distortions arising from the B0 inhomogeneities. One difficulty with this approach is that the generating the field map uses the absolute or total phase, θT, whereas the MRI imaging only produces a residual phase θR, where θR=θT modulo(2π). In other words, θT=θR+N·2π, where N is an integer that varies from one location to another. Accordingly, this approach tries to perform a phase “unwrapping” process, in effect, to determine the value of N across the image, which then allows the total phase θT to be determined from the residual phase θR. Once the total phase has been obtained, the field map and hence the B0 inhomogeneities can be determined, and the image undistorted as appropriate.
Some known systems use a combination of both the first (image-based) and second (filed map-based) techniques. For example, [14] describes an approach in which a field map-based technique is used first to undistort an acquired image, and the undistorted image produced in this manner is then registered, using an intensity based approach, to an earlier (prior) image which was obtained without distortion. Although such an approach has been reasonably effective, the computational demands tend to be high, which means that it is difficult to support real-time image-assisted surgery (for example). Moreover, it continues to be desirable to remove distortion due to B0 inhomogeneities from MRI images as accurately as possible.
2. Review of Some Existing Work
Echo planar imaging (EPI) provides high temporal resolution and is routinely used in functional magnetic resonance imaging (fMRI) and diffusion weighted imaging (DWI) sequences. In recent years, interventional MRI (iMRI) is fast emerging as the preferred imaging choice for image-guided neurosurgery. The relatively high spatial resolution, excellent soft tissue contrast and the lack of ionizing radiation makes iMRI an attractive imaging option for image-guided interventions. Furthermore, along with conventional structural imaging, current commercial iMRI scanners can also perform diffusion and functional imaging which allows for imaging of eloquent brain areas and critical white matter tracts along with the surgical target areas. Modern interventional MRI scanners use EPI sequences to acquire DWI images during neurosurgery, which can be then used for localisation of critical white matter tracts that lie close to the area of intervention. EPI performs fast imaging by sampling the entire frequency space of the selected slice with one excitation pulse and fast gradient blipping. However, this results in very low bandwidth in the phase encoding direction, which makes EPI images highly susceptible to small perturbations of the magnetic field, giving rise to various artefacts arising due to magnetic field inhomogeneities. The primary source of these so-called susceptibility artefacts is the difference in magnetic susceptibility between various tissues being imaged. In the context of neuroimaging, this leads to severe geometric and intensity distortions in areas like the brain stem, frontal and temporal lobes. The distortions are especially severe as the surgically resected cavity contains air and induces high susceptibility differences leading to large distortions around the area of resection. Recent works have shown that diffusion weighted MRI images along with structural images could more accurately localise brain structures of interest during neurosurgical procedures [1], [2]. There is also an interest in performing tractography on interventional DWI images to segment white matter structures of interest [3]-[5]. Hence, it is important to accurately compensate for susceptibility artefacts to be able to use EPI images for effective neuronavigation.
Correction of susceptibility induced distortions in EPI images falls under two broad categories: field map estimation and non-linear image registration. The field map estimation approach is the estimation of B0 magnetic field inhomogeneity at every voxel from phase images acquired at different echo times as shown in [6]-[8]. It was shown in [9] that correction of susceptibility artefacts by field maps is not entirely accurate in regions of high field inhomogeneity. This is especially critical when correcting EPI images that are acquired using interventional MRI during a neurosurgical procedure. The area of resection often lies in close proximity to critical white matter tracts and as the neurosurgical procedure progresses, information on the exact location of the tract is beneficial for surgical outcome. However it is exactly at the resection margin with the brain/air interface that the B0 magnetic field is most inhomogeneous and produces maximum geometric and intensity distortions.
A popular alternative to field maps is to use intensity based non-rigid image registration techniques to register the distorted EPI image to a high resolution undistorted T1-weighted MRI [10]-[13]. However, the EPI images acquired interventionally have low signal-to-noise ratio and suffer from various artefacts which makes intensity based image registration challenging. A recent work [14], an extension of [15], proposed generation of field map estimates from structural images, which was then used to sample a non-uniform B-spline grid for an elastic registration based correction step. However, this work is difficult to apply in the interventional setting due to the complex physical environment around the resection area and the need for tissue segmentation maps. Registration based approaches which require acquisition of an additional EPI image have also been proposed [16], [17]. However, these approaches add to the scan time during neurosurgery.